The Cardinals commissioned the statue after McGwire hit 70 homers in 1998, obliterating Roger Maris' 37-year-old record. There's a place set aside for it alongside other mini-monuments to Cardinals legends outside Busch Stadium.
But the bronze is draped in cloth, hidden in a downtown warehouse. Its place in the limelight has been thrown into question, like so much of McGwire's legacy, by suspicion that steroid use enhanced his career.
McGwire hit 583 homers, seventh on the career list. But he was named on only 23.5 percent of the ballots this January in his first year of eligibility for the Hall of Fame, far short of the 75 percent necessary to be enshrined.
Cardinals president Mark Lamping said team policy is that statues are reserved for Hall of Famers whose numbers have been retired. An exception is Kenny Boyer's No. 14, retired in 1984 even though he did not make it to the Hall.
Sculptor Harry Weber said the statue was commissioned in 2002, the year after McGwire retired.
Weber said Cardinals chairman Bill DeWitt gave him the go-ahead at a dedication ceremony for a statue honoring Hall of Fame shortstop Ozzie Smith.
It seemed obvious then that McGwire would join Smith in the Hall of Fame.
That all changed in 2005, when McGwire was evasive in testimony to Congress regarding steroid use in baseball.
Making the sculpture took months for Weber and a team of welders, masons and artists. Now the labor of love is hidden in an undisclosed location.
The Cardinals own it, Weber said, and don't want anyone taking a peek.
The statue of McGwire began as a series of sketches, catching him from different angles as he unleashed his swing. Weber found McGwire easier to sketch than many subjects because so many fans snapped photos during his historic home run chase in 1998.
Weber used the shots to get a 360-degree picture of McGwire's stance. He then carved a miniature version of the sculpture - called a maquette - which he used as a model for the final piece.
The small statue captures McGwire on his follow-through. Both feet are planted firmly on the ground, and the bat is swinging fast behind McGwire's head.
The version that remains under wraps is three-quarters life-sized. Statues are always a little bigger or a little smaller than normal people, Weber said, because he believes life-sized replicas are "just weird" to look at.
The larger sculpture was then cast in silicon to make a mold for a resin version. The final version was cast in bronze, Weber said.
He declined to say how much the Cardinals paid for the statue.